- There’s a good chance we’ll move rooms (around the corner in ECCR), which would allow me to let the waitlist of students into the class. I will report more on this when I know more (perhaps Tuesday). It is not for sure.
- Please complete the when2meet poll with your availability for office hours. The link & explanation for the poll is available as an announcement in canvas (I didn’t want to put it on a public site).
- Allow me to remind you of the last proposition from class, which was this (restated here a little differently):

Proposition. Let a and b be integers. Then, for some integer k, define the quantity c = a + kb. Then gcd(a,b) = gcd(b,c).

- Suppose you want to compute the gcd of 1925 and 931. The Proposition lets you make a “move” that replaces that big problem with a smaller one. For example, using k=-2, we get c=63 and learn that:

gcd(1925, 931) = gcd(931, 63)

- So, by clever choices of moves, we can replace the original big problem with smaller and smaller ones, until the gcd is obvious. We can go like this:

gcd(1925, 931) = gcd(931, 63) = gcd(63,49) = gcd(49,14) = gcd(14,7) = gcd(7,0) = 7

- First, please verify the set of moves above (recreate it for yourself).
- Your task is to find the “slickest” / “fastest” series of moves to discover the
**gcd of 4181 and 6765**that you can. On Wednesday bring it to class and we will see who can get to the gcd in the fewest moves (when you get to gcd(a,0)=a, you are done). - Please read all of Chapter 0 in your textbook (you have already read a selection; now please finish it).
- There’s a new static page called “Homework” on the website. Please read and understand the honor code rules and general rules there. Email me if you have any questions.
- Your homework due Friday, January 25th is now assigned on that page. Don’t forget that regular homework assignments are assigned each Friday due the following Friday.